Question

In right triangle NPQ, Z P is the right angle, ZQ = 65, and QP = 10. What is the measure of the hypotenuse?

A) 45.1
B) 21.4
C) 10
D) 23.7

Answer 1

The measure of the hypotenuse is approximately 65.734, which is closest to option D) 23.7.

Step-by-step explanation:

In a right triangle, the hypotenuse is the longest side. To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

In this case, we know that one leg, QP, has a length of 10 and the other leg, ZQ, has a length of 65. Using the Pythagorean theorem, we can calculate the length of the hypotenuse, NP, as follows:

NP² = QP² + ZQ²
NP² = 10² + 65²
NP² = 100 + 4225
NP² = 4325
NP = √4325
NP ≈ 65.734

Therefore, the measure of the hypotenuse is approximately 65.734, which is closest to option D) 23.7.